1. Field of the Invention
This Nonprovisional application claims priority under 35 U.S.C. 119(a) on Patent Application No. 2003-124129 filed in Japan on Apr. 28, 2003, respectively, the entire contents of which are hereby incorporated by reference.
The present invention relates to a method of simulating a rolling tire which is capable of analyzing vibration characteristics during rolling on a road with high accuracy.
2. Related Art
In recent years, a computer simulation has been used for development of a tire. The computer simulation enables performance to some extent to be predicted without experimentally manufacturing the tire. As the computer simulation has been known, for example, a rolling simulation, in which a tire model is made to roll on a road model. Each model consists of finite elements. With this simulation, the vibration characteristic of the tire can be predicted by obtaining a time history of a vertical force inputted into a tire axis of the rolling tire model.
FIG. 14 is a side view partly showing a visualized tire model. Small three-dimensional elements e . . . are sequentially arranged in a tire circumferential direction at a tread surface a of the tire model. Each of the three-dimensional elements e . . . consists of a tetrahedral or hexahedral solid element or the like. The surface of each of the elements is flat. Therefore, the tread surface “a” of the tire model and a belt model, not shown, defined inside thereof are not formed into a perfect circle but a regular polygonal shape, as viewed from the side.
FIG. 11B is a graph showing the results of a simulation, in which the above-described tire model is made to roll on a road model at a constant running speed. This graph shows the results of a frequency-analysis of the time history of the vertical force inputted into the tire axis of the tire model, wherein the horizontal axis designates a frequency while a vertical axis designates a gain value thereof. As is clear from FIG. 11B, it is found that the simulation results include a peak vibration component NP, which should not have been generated in an actual tire. The peak vibration component NP is considered to be generated by summing forces for periodically lifting up vertexes “et” of the polygonal shape defined by the tread surface “a” of the tire model from the surface of the road every time the vertex collides with a road model.
It has been found that a frequency Ft of the peak vibration component NP is uniquely determined in accordance with Equation (1) below. It is not preferable that the analysis results include a vibration noise having the above-described peak.Ft (Hz)=N×R  (1)
Here, reference character “N” is the number of elements, which have a great rigidity and are arranged in the tire circumferential direction, of the tire model exemplified by an element made of tread rubber or an element consisting of a belt layer; and reference character “R” is a rotating speed per second of the tire model determined by a running speed V and an outer diameter of the tire model.
The tire model can be more formed into a perfect circle by increasing the number “N” of elements of the tire circumferential direction. However, such a method only transfers the frequency Ft to a high frequency region. Furthermore, the increase in the number “N” of elements markedly prolongs a calculation time of the simulation.